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Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Formula

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Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end. Check FAQs

θ = \frac{τ \cdot L}{C \cdot J shaft}

θ - Angle of twist?τ - Torque Exerted on Wheel?L - Length of Shaft?C - Modulus of Rigidity?J_shaft - Polar Moment of Inertia of shaft?

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Example

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Here is how the Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity equation looks like with Values.

Here is how the Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity equation looks like with Units.

Here is how the Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity equation looks like.

4.2E-10 = \frac{50 \cdot 7000}{84000 \cdot 10}

4.2E-10 = \frac{50N*m \cdot 7000mm}{84000N/mm² \cdot 10m⁴}

4.2E-10 = \frac{50 \cdot 7000}{84000 \cdot 10}

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Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Solution

Follow our step by step solution on how to calculate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

FIRST Step Consider the formula

θ = \frac{τ \cdot L}{C \cdot J shaft}

Next Step Substitute values of Variables

∴

θ = \frac{50N*m \cdot 7000mm}{84000N/mm² \cdot 10m⁴}

Next Step Convert Units

∴

θ = \frac{50N*m \cdot 7m}{8.4E+10Pa \cdot 10m⁴}

Next Step Prepare to Evaluate

∴

θ = \frac{50 \cdot 7}{8.4E+10 \cdot 10}

Next Step Evaluate

∴

θ = 4.16666666666667E-10

LAST Step Rounding Answer

∴

θ = 4.2E-10

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Formula Elements

Variables

Angle of twist

Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

Symbol: θ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Angle of twist

Torque Exerted on Wheel

Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.

Symbol: τ

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Torque Exerted on Wheel

Length of Shaft

The Length of Shaft is the distance between two ends of shaft.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Modulus of Rigidity

Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

Symbol: C

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Polar Moment of Inertia of shaft

Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

Symbol: J_shaft

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia of shaft

Other formulas in Expression for Torque in terms of Polar Moment of Inertia category

Go Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia

C = \frac{τ \cdot L}{θ \cdot J shaft}

Go Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

J shaft = \frac{τ \cdot L}{C \cdot θ}

Go Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

L = \frac{C \cdot θ \cdot J shaft}{τ}

Go Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity

τ = \frac{C \cdot θ \cdot J shaft}{L}

How to Evaluate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity evaluator uses Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft) to evaluate the Angle of twist, Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the angle through which the fixed end of a shaft rotates with respect to the free end. Angle of twist is denoted by θ symbol.

How to evaluate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity using this online evaluator? To use this online evaluator for Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity, enter Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Polar Moment of Inertia of shaft (J_shaft) and hit the calculate button.

FAQs on Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

What is the formula to find Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

The formula of Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity is expressed as Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft). Here is an example- 4.2E-10 = (50*7)/(84000000000*10).

How to calculate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

With Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Polar Moment of Inertia of shaft (J_shaft) we can find Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity using the formula - Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft).

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Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Formula

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Example

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Solution

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Formula Elements

Other formulas in Expression for Torque in terms of Polar Moment of Inertia category

How to Evaluate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

FAQs on Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

Variable Name